Lecture 07 M.S.

• Queuing Theory/Queueing theory- the mathematical study of the formation, function, and congestion of waiting lines, or queues
• Queuing situation involves two parts:

  1. Customer, job, or request - someone or something that request a service
  2. Server - someone or something that completes or delivers the services
• Label the Queueing Situation

  A) Population of Customers

  B) Arrival

  C) Queue

  D) Server

  E) Output

  
• Queueing Discipline - the rules of the queue, for example whether it behaves based on a principle of first in-first out, last-in-first-out, prioritized or serve-in-random-order
• Agner Krarup Erlang - Danish mathematician and engineer
• Early 20th Century - is when the Queueing Theory was introduced
• Erlang worked for Copenhagen Telephone Exchange and wanted to analyze and optimize its operations
• Telephone Waiting Times - Erlang's mathematical analysis paper in 1920, it served as the foundation of applied queuing theory
• Queuing Theory has been applied, just to name a few, to:

  • telecommunication
  • transportation
  • logistics
  • finance
  • emergency services
  • computing
  • industrial engineering
  • project management
• Waiting in Line - a part of everyday life because as a process it has several important functions.
• Queues - a fair and essential way of dealing with the flow of customers when there are limited resources.
• what will be the outcome if a queue process isn't established to deal with overcapacity

  Negative Outcome
• Main Advantage of Queuing Theory

  • business can develop more efficient systems, processes, pricing mechanism, staffing solutions, and arrival management strategies to reduce customer wait times and increase the number of the customers that can be served.
• Limitation of Queuing Theory

  • Possibility that the waiting space may in fact be limited
  • another possibility that arrival rate is state dependent.
  • Customers are discouraged from entering if they observe a long line at the time they arrive.
• Solution of Counter Utilization Level for Utilization Factor

  = Arrival Rate/Service Rate
• Solution for Average no, of customers in Service

  = Arrival Rate/Service Rate-Arrival Rate
• Solution for Average no. of customers in queue

  =Utilization Factor x Average no. of customers in Services
• Solution for Expected Average waiting of the customers in the system/service

  =1/Service Rate-Arrival Rate
• Solution for Expected average waiting time in the queue

  =Utilization Factor x Average waiting time of the customers in the system
• Solution for Idle Probability


  = 1 - Utilization Factor
• Solution of Busy Probability

  =Utilization Factor